22,669 research outputs found
Euler Integration of Gaussian Random Fields and Persistent Homology
In this paper we extend the notion of the Euler characteristic to persistent
homology and give the relationship between the Euler integral of a function and
the Euler characteristic of the function's persistent homology. We then proceed
to compute the expected Euler integral of a Gaussian random field using the
Gaussian kinematic formula and obtain a simple closed form expression. This
results in the first explicitly computable mean of a quantitative descriptor
for the persistent homology of a Gaussian random field.Comment: 21 pages, 1 figur
Finite cosmology and a CMB cold spot
The standard cosmological model posits a spatially flat universe of infinite
extent. However, no observation, even in principle, could verify that the
matter extends to infinity. In this work we model the universe as a finite
spherical ball of dust and dark energy, and obtain a lower limit estimate of
its mass and present size: the mass is at least 5 x 10^23 solar masses and the
present radius is at least 50 Gly. If we are not too far from the dust-ball
edge we might expect to see a cold spot in the cosmic microwave background, and
there might be suppression of the low multipoles in the angular power spectrum.
Thus the model may be testable, at least in principle. We also obtain and
discuss the geometry exterior to the dust ball; it is Schwarzschild-de Sitter
with a naked singularity, and provides an interesting picture of cosmogenesis.
Finally we briefly sketch how radiation and inflation eras may be incorporated
into the model.Comment: 20 pages, 12 figure
Nondispersive X-ray emission analysis for geochemical exploration
Nondispersive X-ray emission technique uses lightweight, and rugged X-ray fluorescence units. The X-ray pulse-height spectra is excited by radioactive isotope sources. The technique is applicable for quantitative and qualitative analyses on complex chemical systems, and satisfies the goals for a lunar geochemical exploration device
A method of solving sets of nonlinear algebraic equations Progress report
Methods for solving nonlinear algebraic equations in computer programs for nuclear magnetic resonance spectroscop
A Shape Theorem for Riemannian First-Passage Percolation
Riemannian first-passage percolation (FPP) is a continuum model, with a
distance function arising from a random Riemannian metric in . Our main
result is a shape theorem for this model, which says that large balls under
this metric converge to a deterministic shape under rescaling. As a
consequence, we show that smooth random Riemannian metrics are geodesically
complete with probability one
Weyl Geometry as Characterization of Space-Time
Motivated by an axiomatic approach to characterize space-time it is
investigated a reformulation of Einstein's gravity where the pseudo-riemannian
geometry is substituted by a Weyl one. It is presented the main properties of
the Weyl geometry and it is shown that it gives extra contributions to the
trajectories of test particles, serving as one more motivation to study general
relativity in Weyl geometry. It is introduced its variational formalism and it
is established the coupling with other physical fields in such a way that the
theory acquires a gauge symmetry for the geometrical fields. It is shown that
this symmetry is still present for the red-shift and it is concluded that for
cosmological models it opens the possibility that observations can be fully
described by the new geometrical scalar field. It is concluded then that this
reformulation, although representing a theoretical advance, still needs a
complete description of their objects.Comment: 12 page
A constructive approach to the soliton solutions of integrable quadrilateral lattice equations
Scalar multidimensionally consistent quadrilateral lattice equations are
studied. We explore a confluence between the superposition principle for
solutions related by the Backlund transformation, and the method of solving a
Riccati map by exploiting two kn own particular solutions. This leads to an
expression for the N-soliton-type solutions of a generic equation within this
class. As a particular instance we give an explicit N-soliton solution for the
primary model, which is Adler's lattice equation (or Q4).Comment: 22 page
Probability distribution of the maximum of a smooth temporal signal
We present an approximate calculation for the distribution of the maximum of
a smooth stationary temporal signal X(t). As an application, we compute the
persistence exponent associated to the probability that the process remains
below a non-zero level M. When X(t) is a Gaussian process, our results are
expressed explicitly in terms of the two-time correlation function,
f(t)=.Comment: Final version (1 major typo corrected; better introduction). Accepted
in Phys. Rev. Let
Rain estimation from satellites: An examination of the Griffith-Woodley technique
The Griffith-Woodley Technique (GWT) is an approach to estimating precipitation using infrared observations of clouds from geosynchronous satellites. It is examined in three ways: an analysis of the terms in the GWT equations; a case study of infrared imagery portraying convective development over Florida; and the comparison of a simplified equation set and resultant rain map to results using the GWT. The objective is to determine the dominant factors in the calculation of GWT rain estimates. Analysis of a single day's convection over Florida produced a number of significant insights into various terms in the GWT rainfall equations. Due to the definition of clouds by a threshold isotherm the majority of clouds on this day did not go through an idealized life cycle before losing their identity through merger, splitting, etc. As a result, 85% of the clouds had a defined life of 0.5 or 1 h. For these clouds the terms in the GWT which are dependent on cloud life history become essentially constant. The empirically derived ratio of radar echo area to cloud area is given a singular value (0.02) for 43% of the sample, while the rainrate term is 20.7 mmh-1 for 61% of the sample. For 55% of the sampled clouds the temperature weighting term is identically 1.0. Cloud area itself is highly correlated (r=0.88) with GWT computed rain volume. An important, discriminating parameter in the GWT is the temperature defining the coldest 10% cloud area. The analysis further shows that the two dominant parameters in rainfall estimation are the existence of cold cloud and the duration of cloud over a point
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